Details

sample764.0ms

Algorithm

intervals

Results

460.0ms	4468×	body	80	nan
72.0ms	173×	body	640	valid
15.0ms	46×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	22×	body	80	valid
2.0ms	3×	body	1280	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series38.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify229.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune289.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 3.3b

Counts

89 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(+ x (- 1.0 x))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(+ x (- 1.0 x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series31.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(+ x (- 1.0 x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	602	708
1	2429	673
2	5002	673

prune258.0ms

Filtered

86 candidates to 59 candidates (31.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 2.5b

Counts

95 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify79.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	816	1082
1	3586	1020
2	5002	1003

prune324.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Merged error: 2.5b

Counts

118 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.3b	(- (sqrt (+ t 1.0)) (sqrt t))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
48×	`sqrt-prod`
44×	`add-sqr-sqrt`
36×	`cbrt-prod`
27×	`distribute-lft-out`
13×	`swap-sqr`
12×	`add-cube-cbrt` `cbrt-div` `difference-of-squares`
11×	`pow1`
10×	`add-log-exp`
9×	`associate-r` `associate-l` `distribute-lft-out--`
6×	`add-exp-log` `flip3-+` `pow1/3` `flip-+`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

20.0ms	(* (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series51.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify93.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	880	1651
1	3745	1555
2	5001	1437

prune455.0ms

Filtered

130 candidates to 79 candidates (39.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	128	12	140

Merged error: 2.5b

Counts

140 → 12

regimes1.5s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	13611×	body	80	nan
237.0ms	576×	body	640	valid
49.0ms	161×	body	320	valid
10.0ms	42×	body	160	valid
8.0ms	76×	body	80	valid
6.0ms	12×	body	1280	valid

Details

sample764.0ms

simplify25.0ms

prune6.0ms

localize22.0ms

rewrite35.0ms

series38.0ms

simplify229.0ms

prune289.0ms

localize26.0ms

rewrite31.0ms

series31.0ms

simplify53.0ms

prune258.0ms

localize27.0ms

rewrite36.0ms

series43.0ms

simplify79.0ms

prune324.0ms

localize33.0ms

rewrite51.0ms

series51.0ms

simplify93.0ms

prune455.0ms

regimes1.5s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling